Question

When a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500lb. It was also noted that the mean weight of a passenger was assumed to be 140lb. Assume a “worst-­‐case” scenario in which all of the passengers are adult men. Assume the weights of men are normally distributed with a mean of 182.9lb and a standard deviation of 40.8lb.

9. If one man is randomly selected, find the probability that he weighs less than 174lbs.

10. With a load limit of 3500lbs, how many male passengers are allowed if we assume a mean weight of 140lbs.

Be sure to include:

- Math Equation

- Draw the distributions (standard normal distribution and the normal distribution if necessary)

- Write the interpretation

Answer 1

Solution:- Given that mean = 182.9 lb , sd = 40.8

standardize x to z = (x - μ) / σ

a. P(X < 174) = P((X-mean)/sd < (174-182.9)/40.8)
= P(Z < -0.2181)
= 0.4129

b. 3500/140= 25 men